Question

Demonstre que para qualquer x real sen (π/2-x)=cos x

Answer 1

Consideramos provada a diferença de dois arcos:

$sen(\alpha-\beta)=sen \alpha \ . \ cos \beta -sen \beta \ .\ cos \alpha \\ \\ sen(\frac{\pi}{2}-x)=sen \frac{\pi}{2}.cos x - sen x.cos \frac{\pi}{2}= \\ \\ sen(\frac{\pi}{2}-x)=1.cosx-sen x .0 \\ \\ \boxed{sen(\frac{\pi}{2}-x)=cos x}$